Creaming and Dumping : Who on Whom ?

In several countries, some healthcare providers combine public service with practice in their own facilities (dual-job practitioners). According to the existing literature, they are viewed as cream-skimming profitable (low-severity) public patients to the benefit of private practice, causing cost of treatment in the public sector to increase. If true, this is particularly problematic when public provider payment is prospective. However, two facts seem to be neglected. First, cream skimming involves effort and thus does not occur in all circumstances. Second, public providers might have an incentive to select patients too, resulting in dumping of the least profitable (high-severity) patients on the private sector. Thus, average cost of treatment in public hospitals does not have to increase, and might even decrease. This paper derives the conditions under which both creaming and dumping are predicted to occur. JEL Classifications: I11, I18


Introduction
Risk selection by healthcare providers may occur in two ways: providers may prefer patients with expected payment greater than expected cost of treatment (cream skimming), and they may get rid of patients with expected payment less than expected cost (dumping).The incentive to discriminate against high-severity (high-cost) patients arises under prospective payment (e.g.Diagnosis Related Group (DRG) payment), which makes providers bear the risk of excessive cost (Ma, 1994;Newhouse, 1996;Ellis, 1998).This incentive cannot be fully neutralized by risk adjustment because the physician diagnosing a patient is likely to have more information about the patient's future cost than the information contained in the risk-adjustment formula (Newhouse, 1989;Dranove, Kessler, McClellan, & Satterthwaite, 2003).Also, additional effort required in treatment of more difficult and complicated patients might give providers the incentive to avoid them (Newhouse, 1996; Barros & Olivella, 2005).Risk selection both in the guise of cream skimming and dumping is more than a theoretical possibility but has been found in empirical research (Newhouse & Byrne, 1988;Newhouse, 1989;Ellis & McGuire, 1996;Dranove et al., 2003).
Risk selection is usually viewed as a problem characterizing market-oriented rather than public healthcare systems (Le Grand, 1991;Ellis, 1998).Even when discrimination against costly patients is illegal in a market-oriented system, some providers may effectively reject them by claiming that they lack the facilities necessary to treat severe cases (Ma, 1994) or by advising medical staff to convince unprofitable patients to seek care elsewhere (Newhouse, 1996).Providers might also cream skim by concentrating on relatively profitable DRGs (Ma, 1994).As a consequence, providers are predicted to differ substantially with regard to the share of expensive patients treated, while severely ill patients face problems of access to health care (Ellis, 1998).Admittedly, extensive regulation in public systems is designed to inhibit exploitation of unpriced risk heterogeneity, causing providers to be tied up with a patient population in a given geographical area, while regulators decide on the range of facilities and services provided.
Yet it has been argued that within public systems, patients might be subject to selection nevertheless.This possibility arises when public providers purchase services from the private sector with the aim of shortening public sector waiting lists in combination with public sector physicians having a second job in a private practice.These dual-job practitioners (DPs) are suspected to manipulate patient transfers in a way that they receive in private practice only the least severe and thus most profitable of public patients (Barros & Olivella, 2005;Gonzalez, 2005).DPs are said to have the incentive because they receive a fixed salary in the public sector, which serves to insulate them from its financial performance.At the same time, they benefit from the low cost of treatment in their private practice which creates a profit margin given prospective payment.This is argued to increase the risk of deficit for public institutions, which suffer from an increase in the average severity and costliness of their patients whereas private institutions appropriate the surplus from treating the low-severity public patients.This reallocation of surplus is seen as inefficient since it undermines the ability of public providers to perform special functions in the public interest, such as education and research.
The present paper re-examines these claims.It proposes a model that takes into account five facts which seem to have been neglected.First, patient selection generally requires effort and time that alternatively could be used for treating patients or for leisure activities.Second, a decrease in the average severity of patients transferred to private facilities by DPs necessarily leads to an increase in the average severity of patients retained in the public sector, causing non-contractible work effort in public facilities to rise.Therefore, single-job practitioners (SPs) who work exclusively in public hospitals may have an interest in dumping high-severity patients on private providers.Third, SPs can be viewed as residual claimants of the surplus generated by public facilities.While this surplus does not accrue to them as a profit, it does provide resources for research, new equipment, and additional facilities (Rickman & McGuire, 1999).Therefore, SPs have a vested interest in keeping the average cost of treatment low in the presence of prospective payment.This interest is shared by hospital managers, who may instruct SPs to dump high-severity patients on private providers as a way to lower average cost of treatment.Fourth, the inclination of DPs to cream skim is predicted in this paper to be weak if their involvement in the private sector is limited or if their total income is high.
~ 34 ~ Fifth, it is also found that the effectiveness of patient selection must exceed a threshold value for selection to be lucrative.
In sum, the actions of the two groups of providers (DPs and SPs) have opposite effects on the severity of patient cases treated and hence average cost of treatment, resulting in their (partial) cancellation.As a consequence, transfers of public patients to private providers, even in combination with allowing dual job holding, does not necessarily drive up average case severity in the public sector and might in fact decrease it.
The reminder of this paper is structured as follows.Two models of provider behavior are presented in the next section, where cream skimming by DPs versus dumping by SPs is discussed along with optimization by the two types of practitioner.Finally, a conclusion is provided in the last section.

Two Models of Provider Behavior
This section contains two models.One depicts the behavior of providers who work exclusively in a public hospital (SPs).The other model applies to providers who combine public service with private practice (DPs).In principle, a third type could be distinguished, i.e. practitioners working exclusively in the private sector who have the right to send patients to a public hospital.Their incentives were analyzed in detail by Zweifel (1981Zweifel ( , 1982Zweifel ( , & 1985)).However, in this paper the hospitalization decision is already made, permitting to focus on SPs and DPs.Both types aim at maximizing their utility, which is increasing in leisure and income.The decision variable is selection effort.For the SP, one has where   is income and   , leisure.Income   in the public sector is assumed to be fixed, e.g. in the guise of a fixed monthly salary.In particular, it does not vary with treatment effort exerted.This assumption may not hold true in all countries; physicians working in public hospitals may in fact be rewarded for their effort.One way is promotion, the other, having private beds.However, latter comes close to dual practice, blurring the distinction between SPs and DPs.Yet, SPs' effort does vary as a function of length of treatment and intensity (stressfulness, respectively) of the work, which in turn depends on the severity of patients treated (Barros & Olivella, 2005).Accordingly, leisure is defined as total time T minus treatment effort   (proportional to average severity of cases) minus other types of effort   .In particular,   can be seen as effort exerted on patient selection, Turning to the dual practitioner, the utility function of the DP is fully analogous to the one of the SP, where   and   are the DP's income and leisure, respectively.However, his or her income   has two components, one arising from involvement in the public sector and the other, from private practice.The first component is given by     , with   being a dimensionless factor, which parameterises the degree of the DP's involvement in the public sector.Together with income from ~ 35 ~ private practice,   is given by Here,   symbolizes involvement in the private sector.It is worth noticing that, in general,   +   ≠ 1.For example,   = 1 and   > 0 characterize a DP, who while working full time in the public sector, spends additional time in private practice.The parameter r is payments for treating of patients transferred from the public sector.They are reduced by   , the patients' mean severity, on the assumption that cost is proportional to severity.Accordingly, DPs' leisure is given by   =  −   − (    +     ) > 0

Cream Skimming by DPs versus Dumping by SPs
It may be worthwhile to recall a few basic facts about the policy of transferring public patients to the private sector.Patients are referred to a public hospital by their general practitioner.In the hospital they initially contact a designated physician, who upon diagnosing them decides whether they should join a waiting list.To be transferred to a private provider, patients need to satisfy certain eligibility criteria such as the expected length of their waiting time.Private facilities contracting with the public payer cannot refuse to treat any of the transferred patients who are part of the agreed contingent (Wiley, 2005;Gonzalez, 2005;Vrangbaek, Østergren, Birk, & Winblad, 2007).Usually, choice between the public and the private facilities is left to eligible patients.Alternatively, patients may leave the choice to the diagnosing physician, who books treatment according to the available operational capacity and the prioritization rule.
The decision variable of the SP is selection effort   ≥ 0. For simplicity, and following Ma (1994), SPs are assumed to be able to predict exactly the amount of resources required by a patient.In this situation, they have an incentive to dump severe cases on private facilities for two reasons.First, as long as effort   is smaller than the reduction in treatment effort   achieved, they benefit from an increase of leisure [see equation (2)].Second, SPs can be seen as residual claimants to surplus generated by the public provider which can be used for research, new equipment, or facilities (Rickman & McGuire, 1999).While the existing literature on patient selection does not describe how selection is performed in actual practice, SPs can control the composition of patients they remain in charge of by manipulating transfers to private facilities.One way is to break rules governing the booking of patients for treatment, in particular medical prioritization.Another way is to use their informational advantage to influence patients in their choice between the public and private setting.
However, all of this requires effort, denoted by   .

2
Let   > 0 be the effectiveness of selection effort   , decreasing in effort   .Therefore, mean 1 For the sake of simplicity, the relative importance of treatment effort in the private sector and of income derived from it are both reflected by the parameter   .A more general formulation does not change results.severity of patients remaining in the public sector decreases by     .However, DPs try to reduce the mean severity of patients transferred to their private practice by exerting effort   > 0, with effectiveness   , resulting in a reduction by     .Therefore, one has Moreover, for both the SP and the DP, cream skimming and dumping by the other necessarily leads to an increase in the severity of patients treated.Hence,   =  −     +     (7)   =  +     −     (8) where S denotes mean severity in the population.

Optimization by the Two Types of Practitioner
According to labor economics, dual job holding is a response to income constraints such as limited demand for labor and/or standardized work contracts.If there were no constraints in any of the two jobs, individuals would focus exclusively on the preferred one (Perlman, 1966;Shishko & Rostker, 1976).The public healthcare sector abounds with regulations regarding hours of work, which may explain the prevalence of DPs who combine work in public and private practice.Moreover, in healthcare systems with dominance of public hospital care, demand for private services is limited.In terms of the two models, these constraints justify treating the two involvement parameters   and   as exogenous, leaving   and   as the only decision variables of the SP and DP, respectively.

The Single-Job Practitioner
From equation (2), for the SP in the public sector the first-order condition for an interior solution reads, since income   does not depend on effort   .In view of equations ( 2) and (7), equation ( 9) can be rewritten to become  3 Therefore,   > 1 at an interior optimum, while   ≤ 1 everywhere leads to a boundary optimum   = 0.
As a consequence, the SP has an incentive to select patients only if the efficiency of dumping exceeds the critical value ̂ = 1.Otherwise, the SP makes no effort to dump high-severity patients; only for   > 1 does the gain from selection outweigh the effort involved.

The Dual-Job Practitioner
In full analogy to equation ( 9), the first-order condition w.r.t.effort for a DP reads, The distinguishing feature is that for the DP, the mean severity of patients does not only affect leisure, but also income from private practice.In view of equations ( 3) to (5) It is of particular interest to know when there is positive selection effort by the DP, i.e., when equation ( 14) has an interior solution.Denoting by   * the optimum value of   , one indeed finds that at  = 0 (no involvement in private practice),   * = 0 (an optimum on the boundary), as there is no solution to the first-order condition (14) in view of   + 1 > 0. This is consistent with the fact that a DP without involvement in the private practice is actually an SP.As long as   * = 0,   and   remain unchanged while  increases.For sufficiently large , however, the term in square brackets becomes positive and eventually compensates − 1   [unless ( 5) is violated already before].This means that there exists a  above which the DP will exert selection effort.

Does More Involvement in Private Practice Entail an Increase in Selection Effort?
The question to be answered in this section is whether an increase in private practice involvement systematically causes the DP to step up selection effort.In the following an exogenous change  > 0 is considered.Admittedly, at least in the long run,  is a decision variable.At a given point in time, however, an increase in  serves to distinguish between DPs with more and DPs with less relative involvement in private practice.Totally differentiating the first-order condition, one obtains The second-order condition for a maximum, All factors on the right-hand side are positive apart from the expression in big parentheses, which has an indefinite sign.The first term in that expression is negative under the reasonable assumption that the DP does not lose money by working in the private sector,  -  > 0 (an increasing value of  with   fixed means less leisure, By assumption (  * > 0), there is a parameter range where equation ( 14) has a solution.Thus,   *  ≥ 0 and generally,   *  > 0 at least on a finite interval.If there is a solution to the first-order condition, the DP who gets more involved in private practice is predicted to increase selection effort at least over this range of p. Whether there will cease to be solutions of equation (14) for some larger values of , i.e., whether the DP will stop exerting selection effort, depends on the properties of the utility and effectiveness functions.It appears reasonable to assume that   approaches zero as  becomes large because, as explained above, this corresponds to more work and more income, i.e., to a lower valuation of income relative to leisure.Then, if equation ( 14) remains solvable for a large value of , (  + 1)  = (    )/  must decrease (eventually to zero) to compensate for this increase.Conversely, if the first-order condition is only solvable up to a certain maximum value of , there must be two solutions (they might coincide in a borderline case) for equation (14), with (  + 1)  evaluated at   = 0.

5
In sum, the DP is predicted to exert positive selection effort • only above a minimum value of involvement in the private practice -see discussion of equation (25); • only if the positivity requirement on leisure is not violated, which can make selection effort entirely unattractive -see equations ( 5) and (28); • that increases with increasing involvement in the private practice -equation ( 16) and 4 The details of the derivation are provided in appendix A. 5 Details are provided in appendix B.
~ 39 ~ (a) starts decreasing and ceases altogether at some maximum involvement, (b) or keeps increasing if the rate of substitution between income and leisure falls rather slowly with increasing involvement, in which case it is ultimately cut off by (5).
If   |  = 0 exceeds a finite threshold for cream skimming.The exact functional form of this threshold depends on   and its derivative at   * .Due to the positivity requirement for leisure [see equation ( 28)] -the value of  necessary for the DP to become interested in cream skimming may, in fact, become so large that it is above the point where the DP is willing to exert any kind of additional effort.The result is that the DP will not cream skim for any value of .

Discussion
The present paper focuses on a public healthcare system where public patients are transferred from public to private providers with the aim of shortening waiting lists in the public sector.The existing literature claims that under such a policy, dual-job practitioners (DPs), who combine public service with private practice, manipulate patient transfers in a way that only the least severe and thus most profitable of public patients are treated in private practice.This is said to result in an increase in average severity and costliness of patients retained in the public sector.The analysis presented in this paper shows this not necessarily to be the case.Patient selection costs time and effort that alternatively could be used for treating patients or for leisure activities.Specifically, there exists a finite threshold for the DP's involvement in private practice below which patient selection is not lucrative.Above that threshold, selection effort is predicted to increase with increasing involvement in private practice under realistic conditions -but only to some degree.A crucial condition is a sufficiently high effectiveness of DPs' cream-skimming effort.Moreover, physicians working exclusively in the public sector (SPs) in turn have an incentive to dump high-severity patients on the private sector.This is because high-severity patients entail disutility due to additional work and an erosion of margins under DRG-based prospective payment.
The analysis suggests that the effects of cream-skimming efforts by DPs and the dumping efforts by SPs on average severity of those patients who remain in the public sector can cancel each other at least to some extent.While it would go beyond the present paper to formally model the net effect of the two types of effort, a preliminary assessment seems possible.In healthcare systems where hospital care is provided predominantly in the public sector, there are many more SPs than DPs.This has a twofold effect for the mean severity and hence treatment cost of patients treated in the public sector.First, DPs have comparatively limited leverage in influencing average severity and cost in the public sector.Second, this means that their cream-skimming effort has low effectiveness, making it less likely that DPs ever engage in patient selection, as shown in this paper.

Limitations and Conclusions
This analysis is subject to several limitations.First, neither the DP nor the SP are viewed as having special professional ethics, which might be intrinsic or induced be reputation effects.Second, the two types of provider do not anticipate each other's actions, although they usually can identify each other.A more detailed analysis may therefore call for a game-theoretic formulation.Third, the physician's hospitalization decision is viewed as exogenous; however, it may well depend on his or her SP or DP status.Still, the present contribution calls attention to the fact that cream skimming and dumping are not a one-way street, as is often surmised in the existing literature.A particular case may serve to buttress this statement; it is presented without claim to generality.A private clinic in Germany performed more than 1,000 endoprosthetic knee surgeries in 2013, of which 45 percent are partial knee replacement performed mainly by DPs.This rate is much higher than the national average of 10 percent.While substantially more demanding, this innovative alternative to total knee replacement has the great benefit of leaving the cruciate ligaments intact (Willis-Owen, Brust, Alsop, Miraldo, & Cobb, 2009).At the same time, DRG payment for it is much lower than for conventional total knee replacement.The likely reason for the DPs in the private clinic to attract high-cost patients is reputation: countrywide, primary care physicians prefer to send their patients to it, trusting high-volume providers to perform the surgery with a maximum rate of favorable outcomes.

( 5 )
with   denoting other effort (again in particular on patient selection) and (    +     ) total treatment effort.

1
the elasticity of selection effectiveness w.r.t.selection effort.
−   > 0).This negative first term can still be compensated by the remaining terms, which are always positive.

Figure 1 .
Figure 1.  as a function of  if equation (14) has solutions for  >  min 0, is assumed to be satisfied; hence, the sign of The first-order condition can also be interpreted in a different way.For �